Question

${\int }_0^{\pi /4}\cos 2xdx$=$\frac{1}{k}$. Find k

Answer 1

${\int }_0^{\pi /4}\cos 2xdx=\frac{1}{k}$

Let $2x=p.2dx=dp$

as $x\to \frac{\pi }{4}$

$2x\to \frac{\pi }{2}$

as $x\to 0$

$2x\to 0$

$=\frac{1}{2}{\int }_0^{\pi /2}\cos pdp=\frac{1}{2}\sin p{]}_0^{\pi /2}$

$=\frac{1}{2}[1-0]=\frac{1}{2}$

Now $\frac{1}{k}=\frac{1}{2}$

$\therefore k=2$